The present invention relates to a device for cooling a reactor positioned in a vessel that comprises a water space and a steam space, whereby cooling pipes that convey evaporating water extend through the reactor and communicate outside the reactor with the water space at the intake end and with the the steam space at the outflow end. Devices of this type operate by employing evaporating water to divert the heat released by exothermal chemical reactions. This type of heat diversion provides an advantage over cooling with a non-evaporating coolant. Since the water, which evaporates as it flows, will evaporate at practically the same temperature at all points in the reactor, a uniform reaction temperature that is optimum in terms of carrying out the reaction will prevail throughout the reactor. The method also has a drawback, however. The water that is converted into steam is constantly replenished with fresh water. When the temperature of the fresh water drops below the evaporation point, the lower temperature will prevail locally in a certain area of the reactor to the detriment of the reaction in that area.